Don, I'd mimic Greg Cook's set up, I'd want to cantilever the casters out to the sides and drop the base of the dolly and the drill press as close to the ground as possible, like 1/8" or maybe 3/16" max. This gets your center of gravity close to the ground, which is good and it also make a tip over, front to back (assuming the casters are out on the sides) just about impossible, as the bottom of the dolly would rotate into the ground if it was tipped much at all.
Do you have a welder? If you do, some stout angle iron, I'd say 2" wide or so is all you need for the frame of the dolly, make it just a hair wider than the base of the drill press, and if the drill press is NOT exactly square, that is what a 4" angle grinders are for
For the cantilever parts that the casters bolt on to, some 4" wide channel would work.
Might be too much work for you if you don't have the tools etc, so maybe just buying the Fox Mini mobile base would be easier?
This is the mobile base I built for the Phoenix, sure it is WAY over kill, but the motor is right on the floor, and the whole saw is VERY stable with this set up.
Here is the base I built for the Green Meanie, my jointer, again, I know, over kill, but I also know that I'll not be having to build a better base at some point
I think you get the idea, get the wheels cantilevered of to the side, so the weight of the tool rides as low as possible.
Cheers!